/*
* UTMXYToLatLon
*
* Converts x and y coordinates in the Universal Transverse Mercator
* projection to a latitude/longitude pair.
*
* Inputs:
* x - The easting of the point, in meters.
* y - The northing of the point, in meters.
* zone - The UTM zone in which the point lies.
* southhemi - True if the point is in the southern hemisphere;
* false otherwise.
*
* Outputs:
* latlon - A 2-element array containing the latitude and
* longitude of the point, in radians.
*
* Returns:
* The public double does not return a value.
*
*/
public GeographicCoordinate UtmXyToLatLon(CartecianCoordinate utm, int zone, bool southhemi)
{
var x = utm.X - 500000.0;
x = x / UTMScaleFactor;
/* If in southern hemisphere, adjust y accordingly. */
var y = utm.Y;
if (southhemi)
{
y -= 10000000.0;
}
y = y/ UTMScaleFactor;
var cmeridian = UtmCentralMeridian(zone);
return MapXyToLatLon(new CartecianCoordinate(x,y), cmeridian);
}
/*
* MapXYToLatLon
*
* Converts x and y coordinates in the Transverse Mercator projection to
* a latitude/longitude pair. Note that Transverse Mercator is not
* the same as UTM; a scale factor is required to convert between them.
*
* Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
* GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
*
* Inputs:
* x - The easting of the point, in meters.
* y - The northing of the point, in meters.
* lambda0 - Longitude of the central meridian to be used, in radians.
*
* Outputs:
* philambda - A 2-element containing the latitude and longitude
* in radians.
*
* Returns:
* The public double does not return a value.
*
* Remarks:
* The local variables Nf, nuf2, tf, and tf2 serve the same purpose as
* N, nu2, t, and t2 in MapLatLonToXY, but they are computed with respect
* to the footpoint latitude phif.
*
* x1frac, x2frac, x2poly, x3poly, etc. are to enhance readability and
* to optimize computations.
*
*/
public GeographicCoordinate MapXyToLatLon(CartecianCoordinate xy, double lambda0)
{
/* Get the value of phif, the footpoint latitude. */
var phif = FootpointLatitude(xy.Y);
/* Precalculate ep2 */
var ep2 = (Math.Pow(sm_a, 2.0) - Math.Pow(sm_b, 2.0)) / Math.Pow(sm_b, 2.0);
/* Precalculate cos (phif) */
var cf = Math.Cos(phif);
/* Precalculate nuf2 */
var nuf2 = ep2 * Math.Pow(cf, 2.0);
/* Precalculate Nf and initialize Nfpow */
var Nf = Math.Pow(sm_a, 2.0) / (sm_b * Math.Sqrt(1 + nuf2));
var Nfpow = Nf;
/* Precalculate tf */
var tf = Math.Tan(phif);
var tf2 = tf * tf;
var tf4 = tf2 * tf2;
/* Precalculate fractional coefficients for x**n in the equations
below to simplify the expressions for latitude and longitude. */
var x1frac = 1.0 / (Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**2) */
var x2frac = tf / (2.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**3) */
var x3frac = 1.0 / (6.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**4) */
var x4frac = tf / (24.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**5) */
var x5frac = 1.0 / (120.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**6) */
var x6frac = tf / (720.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**7) */
var x7frac = 1.0 / (5040.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**8) */
var x8frac = tf / (40320.0 * Nfpow);
/* Precalculate polynomial coefficients for x**n.
-- x**1 does not have a polynomial coefficient. */
var x2poly = -1.0 - nuf2;
var x3poly = -1.0 - 2 * tf2 - nuf2;
var x4poly = 5.0 + 3.0 * tf2 + 6.0 * nuf2 - 6.0 * tf2 * nuf2
- 3.0 * (nuf2 * nuf2) - 9.0 * tf2 * (nuf2 * nuf2);
var x5poly = 5.0 + 28.0 * tf2 + 24.0 * tf4 + 6.0 * nuf2 + 8.0 * tf2 * nuf2;
var x6poly = -61.0 - 90.0 * tf2 - 45.0 * tf4 - 107.0 * nuf2 + 162.0 * tf2 * nuf2;
var x7poly = -61.0 - 662.0 * tf2 - 1320.0 * tf4 - 720.0 * (tf4 * tf2);
var x8poly = 1385.0 + 3633.0 * tf2 + 4095.0 * tf4 + 1575 * (tf4 * tf2);
/* Calculate latitude */
var lat = phif + x2frac * x2poly * (xy.X * xy.X)
+ x4frac * x4poly * Math.Pow(xy.X, 4.0)
+ x6frac * x6poly * Math.Pow(xy.X, 6.0)
+ x8frac * x8poly * Math.Pow(xy.X, 8.0);
/* Calculate longitude */
var lon = lambda0 + x1frac * xy.X
+ x3frac * x3poly * Math.Pow(xy.X, 3.0)
+ x5frac * x5poly * Math.Pow(xy.X, 5.0)
+ x7frac * x7poly * Math.Pow(xy.X, 7.0);
return new GeographicCoordinate(RadToDeg(lon), RadToDeg(lat));
}